Question

For the real-valued functions f(x) =x²+4 and g(x)=x-5, find the composition fog and specify its domain using Interval notation.0/0(9)() = 0

Answer 1

The functions given in the question are

`\begin{gathered} f(x)=x^2+4 \\ g(x)=x-5 \end{gathered}`

To calculate fog(x) we will have to substitue the value of x in f(x) to be x-5

`\begin{gathered} \text{fog(x)}=(x-5)^2+4 \\ \text{fog(x)}=(x-5)(x-5)+4 \\ \text{fog(x)}=x^2-5x-5x+25+4 \\ \text{fog(x)}=x^2-10x+29 \end{gathered}`

The domain of a quadratic ifunction is a set of all real numbers, in interval notation, it is denoted as

[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: -\infty\: