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Find the domain and range of f(x)=1/(x+8)+5?

+2 votes
I've been able to find the domain, but its been so long that I just can't figure out the range. I'm coming here as my last hope. Please if you answer can you please explain how you found out. Thanks
asked Feb 5, 2013 in ALGEBRA 1 by futai Scholar

1 Answer

+1 vote

f(x) = 1/(x + 8) + 5

Rewrite the expression with common denominator.

f(x) = [1 + 5(x + 8)] / (x + 8)

f(x) = [1 + 5x + 40] / (x + 8)

f(x) = (5x + 41) / (x + 8)

x + 8 is not equal to 0 (because of f(x) will turn undefined i.e. infinity)

Therefore x is not equal to -8

domain = x belongs to (-infinity , infinity) - {-8}

for range

f(x) = 1/(x + 8) + 5

Subtract 5 from each side.

f(x) - 5 = 1/(x + 8)

Then x = 1/[f(x) - 5] - 8.

f(x) - 5 is not equal to 0.

therefore f(x) is not equal to 5.

range = ( -infinity , infinity) - {5}

answered Feb 5, 2013 by richardson Scholar

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