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

Question

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

Answer 1

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}