Question

F(x) = √32xg(x) = √2xFind (f .g)(x). Assume x ≥ 0.

Answer 1

Given the functions:

f(x) = √32x

g(x) = √2x

(f .g)(x) means f(x) * g(x)

We get,

`(f\text{ }\cdot\text{ g)(x) = f}(x)\text{ }\cdot\text{ g(x)}`
`\text{ f}(x)\text{ }\cdot\text{ g(x) = }\sqrt[]{32x}\text{ }\cdot\text{ }\sqrt[]{2x}`
`\text{ }\sqrt[]{32x}\text{ }\cdot\text{ }\sqrt[]{2x}\text{ = }\sqrt[]{(32)(2)(x)(x)}`
`\text{ = }\sqrt[]{64x^2}`
`\text{ = }8x`

Therefore, the answer is 8x.