Question

Consider f(x)=4x and g(x) = square root of x^2-1 and h(x)= square root of 16x-1

Answer 1

f(x) = 4x

g(x) =

`\sqrt{x^(2) \: - \: 1 }`

h(x) =

`√(16x \: - \: 1)`

We want to check if h(x) = g(f(x))

So g(f(x)) =

`\sqrt{(4x) {}^(2) - \: 1}`

Simplified;

g(f(x)) =

`\sqrt{16x {}^(2) \: - \: 1 }`

But h(x) =

`√(16x \: - \: 1)`

Hence g(f(x)) is not equal to h(x)