Question

the function f(x)=-4x+9 has a range given by {1, -3, -7, -15, -19, -23} select the domain values of the function from the list. complete the explanation for how you arrived at your answer. btw this isn’t actually a test it’s assigned as hw but please help

Answer 1

Let's see what to do buddy....

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Remember from now on ,

rang = output

and also Remember ,

output = y = f(x)

So : range = f(x)

So we must put the range number instead of f(x) and solve for x.

Let's do it...

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`f(x) = 1`

`- 4x + 9 = 1`

Both sides minus 9

`- 4x = 1 - 9`

`- 4x = - 8`

Negatives simplified

`4x = 8`

Divided both sides by 4

`x = (8)/(4) \\`

`x = 2`

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`f(x) = - 3`

`- 4x + 9 = - 3`

`- 4x = - 3 - 9`

`- 4x = - 12`

`4x = 12`

`x = (12)/(4) \\`

`x = 3`

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`f(x) = - 7`

`- 4x + 9 = - 7`

`- 4x = - 7 - 9`

`- 4x = - 16`

`4x = 16`

`x = (16)/(4) \\`

`x = 4`

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`f(x) = - 15`

`- 4x + 9 = - 15`

`- 4x = - 15 - 9`

`- 4x = - 24`

`4x = 24`

`x = (24)/(4) \\`

`x = 6`

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`f(x) = - 19`

`- 4x + 9 = - 19`

`- 4x = - 19 - 9`

`- 4x = - 28`

`4x = 28`

`x = (28)/(4) \\`

`x = 7`

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`f(x) = - 23`

`- 4x + 9 = - 23`

`- 4x = - 23 - 9`

`- 4x = - 32`

`4x = 32`

`x = (32)/(4) \\`

`x = 8`

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So the domain values are :

x = { 2 , 3 , 4 , 6 , 7 , 8 }

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And we're done.

Thanks for watching buddy good luck.

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