Answer
a) $f(3)=-18$
b) $x=11$
c) $\text{Domain: all real numbers}
\\\text{Range: all real numbers}
$
Work Step by Step
a) To find $f(3),$ substitute $x$ with $3$ in the given function, $f(x)=9x-45.$ Hence,
\begin{array}{l}\require{cancel}
f(x)=9x-45
\\\\
f(3)=9(3)-45
\\\\
f(3)=27-45
\\\\
f(3)=-18
.\end{array}
b) Replace $f(x)$ with $54$ in the given function, $f(x)=9x-45.$ Hence,
\begin{array}{l}\require{cancel}
f(x)=9x-45
\\\\
54=9x-45
\\\\
54+45=9x
\\\\
99=9x
\\\\
\dfrac{99}{9}=x
\\\\
x=11
.\end{array}
c) The domain and the range of linear functions in the form $f(x)=mx+b$ is the set of all real numbers. Hence, the given function has the following characteristics:
\begin{array}{l}\require{cancel}
\text{Domain: all real numbers}
\\\text{Range: all real numbers}
.\end{array}
