Question

Let tan(x) - 2/x. Let g(x) = x^2 + 8. What is f(x)*g(y)?

Answer 1

Answer:

(x tan(x) - 2)(y² + 8) / x

Step-by-step explanation:

It is given,

f(x) = tan(x) - 2/x   &   g(x) = x² + 8

Therefore, we have to find the solution for, f(x) * g(y)

∴ f(x) * g(y)

= (tan(x) - 2/x) (y² + 8)

= (x tan(x) - 2)(y² + 8) / x

Answer 2

Answer:

$f[g(x)]=\frac{(x^2+8)\:tan(x^2+8)-2}{x^2+8}$

$g[f(x)]=\frac{(x\:tanx-2)^2}{x^2}+8$

$f(x)*g(x)=(\frac{(x\:tanx-2)(x^2+8)}{x})$

Step-by-step explanation:

Given:

$f(x)=tanx-\frac{2}{x}=\frac{x\:tanx-2}{x}$

$g(x)=x^2+8$

Now,

$f[g(x)]$

$=f[x^2+8]$

$=\frac{(x^2+8)\:tan(x^2+8)-2}{x^2+8}$

$g[f(x)]$

$=g[\frac{x\:tanx-2}{x}]$

$=(\frac{x\:tanx-2}{x})^2+8$

$=\frac{(x\:tanx-2)^2}{x^2}+8$

$f(x)*g(x)$

$=(\frac{x\:tanx-2}{x})*(x^2+8)$

$=(\frac{(x\:tanx-2)(x^2+8)}{x})$