f(x)=(x+3), h(x)=(3x-5)
Find g(f(x))=h
2 answers
Basically its x+3=3x-5 so subtract x from 3 which gives u 2x then add 5 to the other 3 to balance it out which leaves u 2x=8. Divide each side by 2 and ur g is 4
let g(x) = ax + b
then
g(f(x))
= g(x+3)
= a(x+3) + b
= ax + 3a + b
but we know that
g(f(x)) = 3x - 5
so a = 3 and
3a+b = -5
9+b = -5
b = -14
then g(x) = 3x - 14
check:
g(f(x)) = 3(x+3) - 14
= 3x + 9 - 14
= 3x - 5 = h(x) !!
then
g(f(x))
= g(x+3)
= a(x+3) + b
= ax + 3a + b
but we know that
g(f(x)) = 3x - 5
so a = 3 and
3a+b = -5
9+b = -5
b = -14
then g(x) = 3x - 14
check:
g(f(x)) = 3(x+3) - 14
= 3x + 9 - 14
= 3x - 5 = h(x) !!