Question

Evaluate the function f left parenthesis x right parenthesis equals 7 x plus 5 at the given values of the independent variable and simplify.a.  f left parenthesis negative 9 right parenthesis      b.  f left parenthesis x plus 5 right parenthesis      c.  f left parenthesis negative x right parenthesisa.  f left parenthesis negative 9 right parenthesisequalsnothing (Simplify your answer.)b.  f left parenthesis x plus 5 right parenthesisequalsnothing (Simplify your answer.)c.  f left parenthesis negative x right parenthesisequalsnothing(Simplify your answer.)

Answer 1

The given function is:

`f(x)=7x+5`

a.) To calculate f(-9), substitute x=-9 into the given function and simplify:

`\begin{gathered} f(-9)=7(-9)+5 \\ \Rightarrow f(-9)=-63+5=-58 \end{gathered}`

It follows that f(-9)=-58.

b.) To calculate f(x+5), replace x with x+5 in the given function and then simplify:

`\begin{gathered} f(x+5)=7(x+5)+5 \\ \Rightarrow f(x+5)=7x+35+5 \\ \Rightarrow f(x+5)=7x+40 \end{gathered}`

It follows that f(x+5)=7x+40.

c.) To evaluate f(-x), replace x with -x in the given function and evaluate:

`\begin{gathered} f(-x)=7(-x)+5_{} \\ \Rightarrow f(-x)=-7x+5 \end{gathered}`

Hence, f(-x)=-7x+5.