Question

If k(x)=1.5x^2 -2 and h(x)=1.5^x, find h(k(1.2)

Answer 1

Answer: h(k(1.2)) = 1.067

Explanation:

To solve for the given composite function, we will substitute 1.2 for x into k(x), and then substitute k(1.2) into h(x) for x.

Given:

`\displaystyle k(x)=1.5x^2-2`

Substitute 1.2 for x:

`\displaystyle k(1.2)=1.5(1.2)^2-2`

Substitute k(1.2) for x into h(x):

`h(k(0.16)) = 1.5^(1.5(1.2)^2-2)`

Simplify:

Square -
`h(k(0.16)) = 1.5^(1.5(1.44)-2)`

Multiply -
`h(k(0.16)) = 1.5^(2.16-2)`

Subtract -
`h(k(0.16)) = 1.5^(0.16)`

Power -
`h(k(0.16)) = 1.067025016 \approx 1.067`