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Alik [6]
3 years ago
6

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

Mathematics
2 answers:
laiz [17]3 years ago
6 0
<span>I. f(2) when f(x) = 3x + 2
</span> f(2) = 3(2) + 2=8
 III. 2y + 14 = 4y − 2
 4y- 2y = 14+2
 2y = 16 
 y=16/2=8
<span> statements have the same result</span>
Elan Coil [88]3 years ago
6 0

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.

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