Question

for f(x)=1/x-5 and g(x)=x^2+2 find the expression for g(x) and substitute the value of g(x) into the function in place of x to find the value of f(g(x))

Answer 1

Substituting the expression of g(x) = x^2 + 2 into f(x) = 1/x - 5 gives us f(g(x)) = 1/(x^2 + 2) - 5. This simplifies to -5 - 1/(x^2 + 2).

Step-by-step explanation:

We are given two functions: f(x) = 1/x - 5 and g(x) = x^2 + 2.

We need to find f(g(x)), which means substituting the expression of g(x) into f(x) in place of x.

Substituting g(x) = x^2 + 2 into f(x) = 1/x - 5, we get: f(g(x)) = 1/(x^2 + 2) - 5

Combining terms, we simplify the expression to: f(g(x)) = -5 - 1/(x^2 + 2)

Therefore, the value of f(g(x)) is -5 - 1/(x^2 + 2), depending on the specific value of x used in the function g(x).

Answer 2

f(x) = (1/x) - 5

g(x) = x^2 + 2

=> f[g(x)] = [1/(x^2 +2)] - 5