Question

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

I. f(2) when f(x) = 3x + 2
II. f−1(3) when f(x) = 2 x minus 7, all over 3
III. 2y + 14 = 4y − 2

Answer 1

I. f(2) when f(x) = 3x + 2
 f(2) = 3(2) + 2=8
 III. 2y + 14 = 4y − 2
 4y- 2y = 14+2
 2y = 16 
 y=16/2=8
 statements have the same result

Answer 2

Answer:

All three statements have same results.

Step-by-step explanation:

Statement I: f(2) when f(x) = 3x + 2.

$f(x)=3x+2$

Put x=2.

$f(x)=3(2)+2=8$

The value of the function is 8. It means y=8 at x=2.

Statement II:f⁻¹(3). when f(x) = 2 x minus 7, all over 3.

$f(x)=\frac{2x-7}{3}$

Find the inverse of the function.

Step 1: Substitute f(x)=y

$y=\frac{2x-7}{3}$

Step 2: Interchange x and y.

$x=\frac{2y-7}{3}$

Step 3: Isolate y.

$y=\frac{3x+7}{2}$

Step 4: Substitute y=f⁻¹(x).

$f^{-1}(x)=\frac{3x+7}{2}$

Now, substitute x=3, to find f⁻¹(3).

$f^{-1}(3)=\frac{3(3)+7}{2}=8$

The result of statement II is 8.

Statement III: 2y + 14 = 4y − 2

$2y+14=4y-2$

$14+2=4y-2y$

$16=2y$

$y=8$

The result of statement III is 8.

Therefore all three statements have same results.