Question

Given that f(x) = 2x + 1 and g(x) = −5x + 2, solve for f(g(x)) when x = 3.

A) -91
b) -33
c) -25
d) 35

Answer 1

hint, by definition of compiste function, we can write this:
\[\Large f\left( {g\left( x \right)} \right) = 2g\left( x \right) + 1 = 2\left( { - 5x + 2} \right) + 1 = ...?\]

Answer 2

please continue

Answer 3

do I have to plug something in or just solve?

Answer 4

solve as an algebraic expression

Answer 5

hint:
\[\Large 2\left( { - 5x + 2} \right) + 1 = - 10x + 4 + 1 = ...?\]

Answer 6

it all cancels out. -10x + 4 + 1 = -10x + 4 + 1

Answer 7

now simplify further, what do you get?

Answer 8

4+1=...?

Answer 9

5!!! :)

Answer 10

ok! so we got this:
\[\Large f\left( {g\left( x \right)} \right) = - 10x + 5\]

Answer 11

please substitute x=3 at the right side, what do you get?

Answer 12

f(g(x)) = -25

Answer 13

that's right!

Answer 14

\[f\left( {g\left( 3 \right)} \right) = - 25\]

Answer 15

thank you so much for your help

Answer 16

:)