Question

If f(x) =4x^2 + 1 and g(x) =x2 -5, find (f+g)(x)

Answer 1

The value of $(f+g)(x)$ is $5 x^{2}-4$

Explanation:

Given that the functions $f(x)=4 x^{2}+1$ and $g(x)=x^{2}-5$

We need to determine the value of $(f+g)(x)$

The value of $(f+g)(x)$ can be determined by substituting the value of $f(x)$ and $g(x)$ and simplifying the terms.

Thus, let us assign $f(x)=4 x^{2}+1$ in the function $(f+g)(x)$, we have,

$4 x^{2}+1+g(x)$

Now, let us assign $g(x)=x^{2}-5$ in the function $(f+g)(x)$, we get,

$4 x^{2}+1+x^{2}-5$

Grouping the like terms, we have,

$4 x^{2}+x^{2}+1-5$

Adding the like terms, we get,

$5 x^{2}-4$

Hence, the value of $(f+g)(x)$ is $5 x^{2}-4$