Question
for the given functions $f$ and $g,$ find:$$\begin{array}{llll}{\text { (a) } f \circ g} & {\text { (b) } g \circ f} & {\text { (c) } f \circ f} & {\text { (d) } g \circ g}\end{array}$$State the domain of each composite function.$$f(x)=2 x+3 ; g(x)=3 x$$
Step 1
If we have two functions $f$ and $g$, the composition of $f$ and $g$ is a function that applies $g$ to its input, and then $f$ to the result. It is denoted as $(f \circ g)(x)$, which means $f(g(x))$. Show more…
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For the given functions $f$ and $g,$ find: $$(a) f \circ g$$ $$\text { (b) } g \circ f$$ $$(c) f \circ f$$ $$(d) g \circ g$$ State the domain of each composite function. $$f(x)=2 x+3 ; \quad g(x)=3 x$$
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for the given functions $f$ and $g,$ find: $$ \begin{array}{llll}{\text { (a) } f \circ g} & {\text { (b) } g \circ f} & {\text { (c) } f \circ f} & {\text { (d) } g \circ g}\end{array} $$ State the domain of each composite function. $$ f(x)=\frac{x}{x+3} ; \quad g(x)=\frac{2}{x} $$
For the given functions $f$ and $g,$ find: $$(a) f \circ g$$ $$\text { (b) } g \circ f$$ $$(c) f \circ f$$ $$(d) g \circ g$$ State the domain of each composite function. $$f(x)=\frac{x}{x+3} ; \quad g(x)=\frac{2}{x}$$
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