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Let $f(x)=\frac{1}{x^4+5}$ and $g(x) = \frac{1}{x^2+1}$ . What is the value of $f(1-g(0))$ ?

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Evaluate expression when two complex numbers are given

Full solution

Q. Let

f(x)=\frac{1}{x^4+5}

and

g(x) = \frac{1}{x^2+1}

. What is the value of

f(1-g(0))

?

Calculate $g(0)$ : We are given two functions: $\newline$ $f(x) = \frac{1}{x^4 + 5}$ $\newline$ $g(x) = \frac{1}{x^2 + 1}$ $\newline$ We need to find the value of $f(1 - g(0))$ . $\newline$ First, we will calculate $g(0)$ . $\newline$ Substitute $x = 0$ into $g(x)$ . $\newline$ $g(0) = \frac{1}{0^2 + 1}$ $\newline$ $g(0) = \frac{1}{1}$ $\newline$ $g(0) = 1$
Calculate $1 - g(0)$ : Now that we have $g(0) = 1$ , we will calculate $1 - g(0)$ .
$1 - g(0) = 1 - 1$
$1 - g(0) = 0$
Substitute into $f(x)$ : Next, we will substitute the value of $1 - g(0)$ into $f(x)$ . Since $1 - g(0) = 0$ , we will find $f(0)$ . Substitute $x = 0$ into $f(x)$ . $f(0) = \frac{1}{0^4 + 5}$ $f(0) = \frac{1}{5}$

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