Test 8 Section 3 #15

You’re given:

    \begin{align*}g(x)&=2x-1\\h(x)&=1-g(x)\end{align*}

Then you’re asked for the value of h(0). In function-in-function questions like this, the thing to remember is that you plug in the argument for every appearance of x in a function, including other functions in that function. In other words, because we know that h(x)=1-g(x), we know that h(0)=1-g(0).

And of course, from the first function we’re given, we can calculate the value of g(0):

    \begin{align*}g(x)&=2x-1\\g(0)&=2(0)-1\\g(0)&=-1\end{align*}

Now plug that back into the equation for h(0):

    \begin{align*}h(0)&=1-g(0)\\h(0)&=1-(-1)\\h(0)&=2\end{align*}