SOLUTION: Decide whether or not the functions are inverses of each other. 1] f(x)= 4x+16 and g(x)= 1/4x-4 2] f(x)= sqrt(x+8), domain [-8, infinity); g(x)=x^2+8, domain (-infinity, inf

Question 589966: Decide whether or not the functions are inverses of each other.
1] f(x)= 4x+16 and g(x)= 1/4x-4
2] f(x)= sqrt(x+8), domain [-8, infinity); g(x)=x^2+8, domain (-infinity, infinity)
and last one:
Determine
i) the domain of the function,
ii) the range of the function,
iii) the domain of the inverse, and
iv) the range of the inverse.
f(x) = 2x + 1
I need help understanding these three questions :( Inverses was my least favorite in Algebra! If you could please help, would be greatly appreciated!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Decide whether or not the functions are inverses of each other.
1] f(x)= 4x+16 and g(x)= 1/4x-4
2] f(x)= sqrt(x+8), domain [-8, infinity); g(x)=x^2+8, domain (-infinity, infinity)
and last one:
Determine
i) the domain of the function,
ii) the range of the function,
iii) the domain of the inverse, and
iv) the range of the inverse.
f(x) = 2x + 1
**
1] f(x)= 4x+16 and g(x)= 1/4x-4
(fog)(x)=f[g(x)]=4[(x/4)-4)]+16=x-16+16=x
(gof)(x)=g[f(x)]=(1/4)(4x+16)-4=x+4-4=x
Therefore functions are one-to-one and inverses to each other.
..
2] f(x)= sqrt(x+8), g(x)=x^2+8
f(x) is a one-to-one function but g(x) is not. g(x) is a parabola which is bumped 8 units up and it would fail the horizontal line test as it would have two intersections, that is for a given y, you could have two different x's. These two functions are not inverses of each other.
..
f(x)=2x+1
i) domain:all real numbers or (-∞,∞)
ii) range: (-∞,∞) (This is a straight line with a slope=2 and y-intercept=1.
iii) the domain of the inverse.
x=2y+1
2y=x-1
y^-1=(x-1)/2=x/2-1/2 (This is a straight line with slope=1/2 and y-intercept=-1/2)
domain: (-∞,∞)
iv) range of inverse: (-∞,∞)

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