Question

Let f(x) = x - 2 and g(x) = x2 - 7x - 9. Find f(g(-1)).

Answer 1

so we are to find f(g(-1))
so we notice the inside function is g
and so we want to find g(-1) first

Answer 2

To find g(-1) you will need to use g(x)=x^2-7x-9

Answer 3

notice we want the input to be -1 so we replace all the x's with 1's in g(x)=x^2-7x-9
can you do that?

Answer 4

-1's*

Answer 5

=1^2-7x-9

Answer 6

you need to replace all the x's in g(x)=x^2-7x-9 with -1

Answer 7

not just some

Answer 8

so you should have \[g(-1)=(-1)^2-7(-1)-9\]
can you simplify that?

Answer 9

-2-(-7)-9

Answer 10

(-1)^2=(-1)(-1)
this is not the same as -1-1

Answer 11

or however your reading it
it is not the same as (-1)(2)
(-1)^2 means (-1)(-1)

Answer 12

\(\bf f(x) = x - 2 \qquad {\color{brown}{ g(x)}} = x^2 - 7x - 9
\\ \quad \\
f(\quad {\color{brown}{ g(x)}}\quad )={\color{brown}{ g(x)}}-2\implies f(\quad {\color{brown}{ g(x)}}\quad )=({\color{brown}{ x^2 - 7x - 9}})-2
\\ \quad \\
f(\quad {\color{brown}{ g({\color{blue}{ -1}})}}\quad )=({\color{brown}{ ({\color{blue}{ -1}})^2 - 7({\color{blue}{ -1}}) - 9}})-2\)