Answer:

Step-by-step explanation:
Rewrite Equation.

Simplify.

Simplify.

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

Simplify & Answer:

Answer:
The only pair of functions that are inverses of each other are the ones for option D.
Step-by-step explanation:
Two functions, f(x) and g(x), are inverses if and only if:
f( g(x) ) = x
g( f(x) ) = x
So we need to check that with all the given options.
A)

then:

This is clearly different than x, so f(x) and g(x) are not inverses.
B)
![f(x) = \sqrt[3]{11*x} \\g(x) = (\frac{x}{11} )^3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7B11%2Ax%7D%20%5C%5Cg%28x%29%20%3D%20%28%5Cfrac%7Bx%7D%7B11%7D%20%29%5E3)
Then:
![f(g(x)) = \sqrt[3]{11*(\frac{x}{11})^3 } = \sqrt[3]{\frac{x^3}{11^2} } = \frac{x}{11^{2/3}}](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%5Csqrt%5B3%5D%7B11%2A%28%5Cfrac%7Bx%7D%7B11%7D%29%5E3%20%7D%20%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%5E3%7D%7B11%5E2%7D%20%7D%20%3D%20%5Cfrac%7Bx%7D%7B11%5E%7B2%2F3%7D%7D)
This is different than x, so f(x) and g(x) are not inverses.
C)

Then:

Obviously, this is different than x, so f(x) and g(x) are not inverses.
D)

Then:

In this case we can conclude that f(x) and g(x) are inverses of each other.
Answer:
x= 3/8 = 0.375 , x= -4/5= -0.8
Step-by-step explanation:
8x-3=0
8x=3
8x/8 = 3/8
x= 3/8 converted to decimal will be =0.375
for 5x+4=0
5x= -4
5x/5 = -4/5
x= -4/5 = converted to decimal will be = -0.8
Step-by-step explanation:
When x = 0,
3x + 7
= 3 ( 0 ) + 7
= 0 + 7
= 7
When x = 4,
3x + 7
= 3 ( 4 ) + 7
= 12 + 7
= 19
When x = 8,
3x + 7
= 3 ( 8 ) + 7
= 24 + 7
= 31
When x = 14,
3x + 14
= 3 ( 14 ) + 14
= 14 ( 3 + 1 )
= 14 ( 4 )
= 56