Question

If f(x) = 2x+5 a. if f(a) =20 , what is the value of a? b. if f(b)= 0, what is the value of b?

1) a.- 7.5 b. 2.5
2) a.6.5 b. -1.5
3) a.3.35 b. 2.5
4) a.7.5 b. -2.5

Answer 1

Answer: choice (4)

a = 7.5 and b = -2.5

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Work Shown:

f(x) = 2x+5

f(a) = 2a+5 .... replace every x with 'a'

20 = 2a+5 .... replace f(a) with 20, since f(a) = 20

2a+5 = 20

2a = 20-5 .... subtract 5 from both sides

2a = 15

a = 15/2 ... dividing both sides by 2

a = 7.5

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f(x) = 2x+5

f(b) = 2b+5 ... replace every x with b

0 = 2b+5 .... replace f(b) with 0, since f(b) = 0

2b+5 = 0

2b = -5 .... subtract 5 from both sides

b = -5/2 .... divide both sides by 2

b = -2.5

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We have a = 7.5 and b = -2.5. So we go for choice (4)

Answer 2

Given :-

• f(x) = 2x + 5
• f(a) = 20
• f(b) = 0

To Find :-

• The values of a and b .

Solution :-

Here we are given that ,

`f(x) = 2x + 5`

Substituting x = a , we have ,

`f(a) = 2a + 5`

Now f(a) = 20 . So ,

`20 = 2a + 5`

Solve out for a ,

`20 - 5 = 2a\\`

`2a = 15\\`

`a = (15)/(2)= 7.5`

Hence the value of a is 7.5

For finding out the value of b , substitute x = b , and f(b) = 0 ,

`f(b) = 2b + 5 \\`

`0 = 2b + 5`

Solve for b ,

`2b = -5 \\`

`b =(-5)/(2)=-2.5`

Hence the value of b is -2.5

4th option is correct .

I hope this helps.