Question

Given:
f(x)=2x^2-x+1
g(x)=2 sin x
h(x)=3^x

Determine:
a) f(g(x))
b) (h^-1 o f)(x)
c) g(f(h(x))))

Please show steps, thank you very much.

Answer 1

a)
f(g(x))
= f(2sinx)
= 2(4sin^2 x) - 2sinx + 1
= 8sin^2 x - 2sinx + 1

for b) find the inverse of 3^x first
y = 3^x
inverse is x = 3^y
lnx = y ln3
y = (lnx)/ln3
so (h^-1 o f)(x) = ln(2x^2 - x + 1)/ln3

you try the last

Answer 2

2sin(2(3^x)^2 - 3^x + 1)
2sin(2(3^2x) - 3^x + 1) ??

Answer 3

correct!
good job