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zysi [14]
1 year ago
6

Pleas help me find the composition of goh and it’s domain

Mathematics
1 answer:
Ksivusya [100]1 year ago
5 0

Solution:

The function is given below as

\begin{gathered} g(x)=\frac{x+4}{x-1} \\ h(x)=2x-1 \end{gathered}

To figure out

(goh)(x)

To do this , we will substitute x= 2x-1 in g(x)

\begin{gathered} g(x)=\frac{x+4}{x-1} \\ g(h)(x)=\frac{2x-1+4}{2x-1-1} \\ g(h)(x)=\frac{2x+3}{2x-2} \end{gathered}

Hence,

The composte function will be

(goh)(x)=\frac{2x+3}{2x-2}

Step 2:

To figure out the domain,

In mathematics, the domain of a function is the set of inputs accepted by the function.

Hence,

The domain of the function is

\begin{bmatrix}\mathrm{Solution:}\:&\:x1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:1\right)\cup \left(1,\:\infty \:\right)\end{bmatrix}

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