Find the range of the given function with domain D. Find an equation of the form f(x) = mx + b for ?

Question

Find the range of the given function with domain D. g: x → 1 - x², D = {-1 , 0, 1}

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Find an equation of the form f(x) = mx + b for the given linear function.

m = -2; f(4) = -6

f(0) = 5; f(2) = 7

Answer 1

g: x → 1 - x²

That simply means that your function is g(x) = 1 - x²

Now your given its domain.  Therefore, substitute each value of x in D to find the Range:

g(-1) = 0

g(0) = 1

g(1) = 0

Therefore, R = {0, 1}

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You're given the slope therefore, the equation looks like:

f(x) = -2x + b

But we're given that f(4) = -6

Therefore,

f(4) = -2(4) + b = -6

Which yields that b = 2

Therefore, your equation is y = -2x + 2

For the second we get a system of equations:

(1)  f(0) = m(0) + b = 5

(2)  f(2) = m(2) + b = 7

From (1) we get that b = 5.  Substitute that into (2)

2m + 5 = 7

2m = 2

m = 1

Therefore, your equation is y = x + 5.

Hope this helps!