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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

Sagot :

VirαtKσhli

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 ,

[tex] f(x) = 2x + 5 [/tex]

Substituting x = a , we have ,

[tex] f(a) = 2a + 5[/tex]

Now f(a) = 20 . So ,

[tex]20 = 2a + 5 [/tex]

Solve out for a ,

[tex] 20 - 5 = 2a\\[/tex]

[tex] 2a = 15\\[/tex]

[tex] a = \dfrac{15}{2}= 7.5[/tex]

Hence the value of a is 7.5

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

[tex] f(b) = 2b + 5 \\[/tex]

[tex]0 = 2b + 5 [/tex]

Solve for b ,

[tex] 2b = -5 \\[/tex]

[tex] b =\dfrac{-5}{2}=-2.5[/tex]

Hence the value of b is -2.5

4th option is correct .

I hope this helps.

Answer:  choice (4)

a = 7.5 and b = -2.5

=======================================

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

-------------

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

--------------

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

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