Substitute negative three into the function.

\(\displaystyle g(-3)= 2(-3)^3-6(-3)\)

Simplify this equation by order of operations.

\(\displaystyle 2(-3)^3-6(-3) = 2(-27)+18 = -54+18\)

The answer is:  \(\displaystyle -36\)

To solve this question, first convert the given function to its inverse.

Rewrite \(\displaystyle f(x) = 6x+6\) by replacing \(\displaystyle f(x)\) with \(\displaystyle y\).

\(\displaystyle y= 6x+6\)

Interchange the x and y variables.

\(\displaystyle x=6y+6\)

Solve for y.  Subtract 6 from both sides.

\(\displaystyle x-6=6y+6-6\)

Simplify, and divide by 6 on both sides.

\(\displaystyle \frac{x-6}{6}=\frac{6y}{6}\)

Simplify both sides.

The inverse function is:  \(\displaystyle y= f^{-1}(x)= \frac{1}{6}x-1\)

Solve for \(\displaystyle f^{-1}(6)\) by plugging 6 into the inverse function.

\(\displaystyle \frac{1}{6}(6)-1 = 1-1=0\)

The answer is:  \(\displaystyle 0\)

Input \(\displaystyle (2x)\) as the replacement of the x-variable for the function \(\displaystyle f(x)\).

The equation becomes:

\(\displaystyle f(2x) = 3(2x)+9\)

Simplify by distribution.

The answer is:  \(\displaystyle 6x+9\)

Replace the \(\displaystyle f(x)\) with \(\displaystyle y\).

\(\displaystyle y= 3x+3\)

Interchange the x and y variables.

\(\displaystyle x= 3y+3\)

Subtract three from both sides.

\(\displaystyle x-3= 3y+3-3\)

\(\displaystyle x-3= 3y\)

Divide by three on both sides.

\(\displaystyle \frac{x-3}{3}=\frac{ 3y}{3}\)

The inverse function is:  \(\displaystyle y=\frac{1}{3}x-1\)

Substitute \(\displaystyle f^{-1}(3)\) as a replacement of \(\displaystyle x\).

\(\displaystyle y=\frac{1}{3}(3)-1 = 1-1 = 0\)

The answer is:  \(\displaystyle 0\)

Replace x with negative one-fifth.

\(\displaystyle f(-\frac{1}{5})= 5(-\frac{1}{5})-5\)

Simplify the expression.  When a number is subtracted from a 

\(\displaystyle -1-5 = -6\)

The answer is \(\displaystyle -6\).

Evaluate \(\displaystyle g(f(\frac{1}{95}))\) by solving for \(\displaystyle f(\frac{1}{95})\) first.

No matter what value of \(\displaystyle x\), \(\displaystyle f(x) = \frac{1}{95}\).  This means that:

\(\displaystyle f( \frac{1}{95}) = \frac{1}{95}\)

Then:  

\(\displaystyle g(\frac{1}{95})\)

For any value of \(\displaystyle x\), \(\displaystyle g(x) = 95\).  This means that:

\(\displaystyle g(\frac{1}{95}) = 95\)

The answer is:  \(\displaystyle 95\)

To determine the output of \(\displaystyle f(x)\), substitute the value of \(\displaystyle \frac{1}{3}\) as a replacement of \(\displaystyle x\).

\(\displaystyle f(\frac{1}{3})= \frac{1}{2(\frac{1}{3})} = \frac{1}{\frac{2}{3}}\)

Rewrite the complex fraction using a division sign.

\(\displaystyle 1\div \frac{2}{3}\)

Take the reciprocal of the second term and change the division sign to a multiplication sign.

\(\displaystyle 1\div \frac{2}{3} = 1\times \frac{3}{2}\)

The answer is:  \(\displaystyle \frac{3}{2}\)

Substitute three into the function of \(\displaystyle g(x)=3x\) to solve for \(\displaystyle g(3)\).

\(\displaystyle g(3)=3(3)=9\)

Substitute this value into the function \(\displaystyle f(x) = 3\).

\(\displaystyle f(9)=3\)

There is no x-variable to substitute nine, which means the function is equal to three.

The answer is:  \(\displaystyle 3\)

Substitute the assigned values into the expression.

\(\displaystyle 2(x+2y)=2(4+2(6))\)

Simplify the inside parentheses.

\(\displaystyle = 2(4+12) = 2(16) = 32\)

The answer is:  \(\displaystyle 32\)

Substitute the assigned values into the expression.

\(\displaystyle 3b^2-5c^3 = 3(2)^2-5(-1)^3\)

Simplify by order of operations.

\(\displaystyle = 3(4)-5(-1) = 12+5 = 17\)

The answer is:  \(\displaystyle 17\)