Question

Which of the following statements have the same result? Explain each step in solving each one.

Answer 1

Answer:

None of the following statements have the same result.

Step-by-step explanation:

1) f(2) when f(x) = 3x + 4

We just have to put x=2

$f(x)=3x+4\\f(2)=3(2)+4\\f(2)=6+4\\f(2)=10$

So, f(2) when f(x) = 3x + 4 is x=10

2) f⁻¹ (4)  when f(x) =3x-4/5

We need to find f⁻¹(x) first.

Put $y=3x-\frac{4}{5}$

Now solve for x

Add 4/5 on both sides

$y+\frac{4}{5}=3x-\frac{4}{5}\\y+\frac{4}{5}=3x\\x=\frac{1}{3}y+\frac{4}{5*3}\\x=\frac{1}{3}y+\frac{4}{15}\\x=\frac{5y+4}{15}$

Now put  f⁻¹(x)  instead of x and replace y with x

$f^{-1}(x)=\frac{5x+4}{15}$

Now finding f⁻¹(4)

$f^{-1}(x)=\frac{5x+4}{15} \\f^{-1}(4)=\frac{5(4)+4}{15} \\f^{-1}(4)=\frac{20+4}{15} \\f^{-1}(4)=\frac{24}{15}$

f⁻¹ (4)  when f(x) =3x-4/5 is 24/15

3) $3y - 6 = y + 10$

Solving:

$3y - 6 = y + 10\\3y-y=10+6\\2y=16\\y=16/2\\y=8$

Solving 3y − 6 = y + 10, we get y=8

None of the following statements have the same result.