Question

Given that f(x) = −x + 4 and g(x) = −2x − 3, solve for f(g(x)) when x = 2.

A. −14
B.−7
C. 7
D. 11

Answer 1

I'm thinking 11

Answer 2

yes, correct.

Answer 3

Thank you :)

Answer 4

Example Problem:

\(\large\color{#000000 }{ \displaystyle f(x)=3x-5 }\)
\(\large\color{#000000 }{ \displaystyle g(x)=5x+4 }\)

Find f(g(x)) when x=3.

SOLUTION:

your function f(x) is
\(\large\color{#000000 }{ \displaystyle f(\color{red}{x} )=3\color{red}{x}-5 }\)

to find f( g(x) ) you need to plug the g(x) into the f(x), for x.
\(\large\color{#000000 }{ \displaystyle f(\color{red}{g(x)} )=3(\color{red}{g(x)})-5 }\)

But, I know that g(x) is 5x+4, so I can apply this for my right side.

\(\large\color{#000000 }{ \displaystyle f(\color{red}{g(x)} )=3(\color{red}{5x+4})-5 }\)
\(\large\color{#000000 }{ \displaystyle f(\color{red}{g(x)} )=15x+12-5 }\)
\(\large\color{#000000 }{ \displaystyle f(\color{red}{g(x)} )=15x+7 }\)

and when x=3, we get
\(\large\color{#000000 }{ \displaystyle f(\color{red}{g(3)} )=15(3)+7=45+7=52 }\)