f(x) = √x

g(x) = 3x – b

If the graph of y = f(g(x)) passes through (6, 5) in the standard (x, y) coordinate plane, what is the value of b?

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Posts Tagged: functions

# f(x) = √x and g(x) = 3x – b…

# Number 2 on the functions practice questions

# If f(x) = 2x + 3 and f(g(x)) = 8x – 1, which of the following equals g(x)? A) 4x-2 B) 4x-1 C) 8x-4 D) 8x-1 E) 16x+23

# If f(x)=-x+7 and g(f(x))=2x+1 what is the value of g(2) ?? Helppp plzzz

# The function f is defined by f(r) = (r-4)(r+1)^2 . If f(h-3) = 0, what is one possible value for h? I don’t see the correlation between the two functions. Can you please elucidate? Thank you <3

# The function f has the property that, for all x, 3f(x) = f(3x)…

# April 2017 SAT, Section 4 #22

# The figure above shows the graph of the function f(x)=ax +b, where a and b are constants. What is the slope of the graph of the function g(x)=-2f(x)

# The figure above shows the graph of the function f(x)=ax +b, where a and b are constants. What is the slope of the graph of the function g(x)=-2f(x)

Note that f(x) is a line in slope-intercept form, where a is the slope and b is the intercept. Once you recognize that, you just need to know that, notationally, the –2 in front of f(x) means you multiply the whole thing by –2. So: That’s still a line, but now the slope is –2a. from Tumblr (more…)

# If f is a function with the property that f(2x-1)=cx for all x,then f(x) =

# If f and g are functions, where f(x) = x^3 -10x^2 +27x – 18 and g(x) = x^3 – x^2 – 6x…

# Could you please explain SAT Past paper 3, section 4, question 12?

# Can you please explain Question 11, Test 6, section 3?

# I don’t understand a question from your book. Question #2 on functions.

# Test 8 Section 3 #15

f(x) = √x

g(x) = 3x – b

If the graph of y = f(g(x)) passes through (6, 5) in the standard (x, y) coordinate plane, what is the value of b?

I’m having a lot of trouble with this problem, could you please break it down for me? It is number 2 on the functions practice questions. “If f(x-1)=x+1 for all values of x, which of the following is equal to f(x+1)?”

A. x+3

B. x+2

C. x-1

D. x-3

The way to think about this (for me, anyway) begins with understanding that 2[something] + 3 = 8x – 1, and our job is to figure out what that something is. Since this question gives us answer choices, all we really need to do is try each one as the something to see what works. Since (more…)

Think of it this way: the g function is doing SOME AS-YET-UNKNOWN THINGS to (–x + 7) to turn it into (2x + 1). Of the simple mathematical operations probably at play here (addition, subtraction, multiplication, division) what could be going on? First, the only way you go from –x to 2x is you multiply by –2. So (more…)

The thing to remember about functions is that they do the same thing to whatever is inside the parentheses. So don’t worry about the r vs. the h. They could use x, or a little star symbol, or whatever else they want. What matters is that the function f, as defined here, will equal zero (more…)

A function will only have that property if it’s a line that passes through the origin. For example, f(x) = 5x has that property: You can try the same with other linear functions to see why they won’t work. For example, if f(x) = 5x + 2: Nonlinear functions also won’t work. For example, if f(x) (more…)

Thank you, Mike, for your ever-awesome explanations! Here’s a question from April 2017 SAT:

Note that f(x) is a line in slope-intercept form, where a is the slope and b is the intercept. Once you recognize that, you just need to know that, notationally, the –2 in front of f(x) means you multiply the whole thing by –2. So: That’s still a line, but now the slope is –2a. from Tumblr (more…)

A question like this on the SAT will always have answer choices, and in this case would be easy to backsolve. Don’t rob yourself of easy points—remember that answer choices are often a helpful tool! Use them to your advantage. In this case, you’d simply need to plug (2x – 1) in for x in each answer choice (more…)

If f and g are functions, where f(x) = x^3 -10x^2 +27x – 18 and g(x) = x^3 – x^2 – 6x, which of the following gives a relationship between f and g?

A) g(x) = 3 f(x)

B) g(x) = f(x) – 3

C) g(x) = f(x) + 3

D) g(x) = f(x – 3)

E) g(x) = f(x + 3)

Can you solve w/o graphing?

Could you please explain SAT Past paper 3, section 4, question 12? I don’t really understand why the double root is considered a ‘distinct’ zero.

Thank you for your time!

Hi Mike, Can you please explain Question 11, Test 6, section 3 ? I know the parabola opens downward, but I’m confused after that. Thanks.

I don’t understand a question from your book. Question #2 on functions. Could you explain it in more detail?

Test 8 Section 3 #15