First evaluate \(\displaystyle f (17)\) and \(\displaystyle g(17)\), then subtract.

\(\displaystyle f (x) = 3 - \sqrt{x-1}\)

\(\displaystyle f (17) = 3 - \sqrt{17-1} = 3 - \sqrt{16} = 3-4 = -1\)

\(\displaystyle g\left ( x\right ) = 3 + \sqrt{x-1}\)

\(\displaystyle g(17) = 3 + \sqrt{17-1} = 3 + \sqrt{16} = 3+4 = 7\)

\(\displaystyle \left (f-g \right ) (17) = f(17)-g(17) = -1-7 = -8\)

Plug in \(\displaystyle (t+2)\) for \(\displaystyle x\).

 \(\displaystyle f(x) = 2x^2 - 4x +1\)

\(\displaystyle x=t+2\)

\(\displaystyle f(t+2) = 2(t+2)^2 - 4(t+2) +1\)

FOIL the squared term and distribute -4:

\(\displaystyle 2(t^2+2t+2t+4)-4t-2+1\)

Distribute the 2:

\(\displaystyle 2t^2+8t+8-4t-2+1\)

Combine like terms:

\(\displaystyle 2t^2 + 4t + 1\)

Plug in \(\displaystyle A\) as if it were a constant, and then solve for its value:

\(\displaystyle g (A) = 5A +7 = 24\)

\(\displaystyle 5A +7 - 7 = 24-7\)

\(\displaystyle 5A = 17\)

\(\displaystyle 5A \div 5 = 17\div 5\)

\(\displaystyle A = 3.4\)

\(\displaystyle f(x) = \left \lceil x^{2} + x + 2 \right\rceil\)

Plug in 5.5:

\(\displaystyle f(5.5) = \left \lceil 5.5^{2} + 5.5 + 2 \right\rceil\)

\(\displaystyle f(5.5) = \left \lceil 30.25 + 5.5 + 2 \right\rceil\)

\(\displaystyle f(5.5) = \left \lceil 37.75 \right\rceil = 38\)

Plug \(\displaystyle h(x)\) into \(\displaystyle g(x)\).

\(\displaystyle g\left ( x \right ) =2x-3\)

\(\displaystyle g\left ( h\left ( x \right ) \right ) = 2\times h(x) - 3 = 2x^{2} - 3\)

Now plug that into \(\displaystyle f(x)\):

\(\displaystyle f\left ( g\left ( h\left ( x \right ) \right ) \right )= \sqrt{g(h(x))} = \sqrt{2x^{2}-3}\)

Given the equation,

 \(\displaystyle f(x)=5x^3+2x-24\) and  \(\displaystyle x=2\)

Plug in \(\displaystyle 2\) for \(\displaystyle x\) to the equation, \(\displaystyle f(2)=5(2)^3+2(2)-24\) 

Solve and simplify. 

\(\displaystyle f(2)=5(8)+4-24\)

\(\displaystyle f(2)=40+4-24\)

\(\displaystyle f(2)=44-24\)

\(\displaystyle f(2)=20\)

\(\displaystyle f(x)=\frac{4x-2}{x+3}, x\neq-3\)

Plug in the \(\displaystyle x\) value for \(\displaystyle x\).

\(\displaystyle f(0)=\frac{4(0)-2}{(0)+3}\)

Simplify

\(\displaystyle f(0)=\frac{0-2}{3}\)

Subtract

\(\displaystyle f(0)=\frac{-2}{3}\)

On the equation, replace x with 2 and then simplify.

\(\displaystyle y=x^3-4x+9\)

\(\displaystyle y=(2)^3-4(2)+9\)

\(\displaystyle y=8-8+9\)

\(\displaystyle y=9\)

Plug 3 in for x:

  \(\displaystyle f(3)=\frac{(3^{2})+12*3}{3*3}\)

Simplify:

 =  \(\displaystyle \frac{9+36}{9}\)

 = 5

To complete an equation with a  function, plug the number inside the parentheses into the equation for \(\displaystyle x\) and solve algebraically.

In this case the \(\displaystyle f(7)=7^{2}+(15*7)+35\)

Square the 7 and multiply to get \(\displaystyle f(7)=49+105+35\)

Add the numbers to get the answer \(\displaystyle f(7)=189\).