Hi! May you please explain how to find the function for f(x) for number 5 from the practice questions in the “functions” chapter? I saw the solution, which said to find f(5+3), and then I got the correct answer, but I wanted to see if there is a function that could be found (as I tried to find it but I found it incorrectly and got an incorrect answer).

# How do you do Test 9 section 3 number 20?

How do you do Test 9 section 3 number 20?

# test 9 section 3 number 18

test 9 section 3 number 18

# f(x) = √x and g(x) = 3x – b…

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?

# Number 2 on the functions practice questions

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

# 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

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…)

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

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 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 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…)

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

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…)

# April 2017 SAT, Section 4 #22

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

# 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…)

# 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) =

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…

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?

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!