About Determine if Two Functions are Inverses:
If two functions f(x) and g(x) are inverses, then it must be true that f(g(x)) = x and g(f(x)) = x. If one of these conditions fails, we can report that they are not inverses. We must check both in order to say that our two functions f and g are inverses.
Test Objectives
- Demonstrate an understanding of function composition
- Demonstrate the ability to determine if two functions are inverses
#1:
Instructions: determine if the given functions f(x) and g(x) are inverses.
$$a)\hspace{.2em}$$ $$f(x)=\frac{3}{x - 1}- 1$$ $$g(x)=\frac{3}{x + 1}+ 1$$
$$b)\hspace{.2em}$$ $$f(x)=\frac{4}{x}- 3$$ $$g(x)=\frac{4}{x + 3}$$
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: determine if the given functions f(x) and g(x) are inverses.
$$a)\hspace{.2em}$$ $$f(x)=\frac{1}{x - 1}$$ $$g(x)=\frac{4}{x - 2}- 1$$
$$b)\hspace{.2em}$$ $$f(x)=(x + 1)^3 + 1$$ $$g(x)=\sqrt[3]{x - 1}- 1$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Instructions: determine if the given functions f(x) and g(x) are inverses.
$$a)\hspace{.2em}$$ $$f(x)=\sqrt[3]{x - 2}- 2$$ $$g(x)=-x^3 + 4$$
$$b)\hspace{.2em}$$ $$f(x)=1 + \frac{1}{2}x$$ $$g(x)=2x - 2$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: determine if the given functions f(x) and g(x) are inverses.
$$a)\hspace{.2em}$$ $$f(x)=\sqrt[5]{x - 1}$$ $$g(x)=x^5 + 1$$
$$b)\hspace{.2em}$$ $$f(x)=-\frac{\sqrt[3]{4x}}{2}$$ $$g(x)=\sqrt[5]{x - 2}+ 2$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: determine if the given functions f(x) and g(x) are inverses.
$$a)\hspace{.2em}$$ $$f(x)=x + 5$$ $$g(x)=x - 5$$
$$b)\hspace{.2em}$$ $$f(x)=\frac{x - 3}{x + 7}$$ $$g(x)=\frac{x - 7}{x + 3}$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
a) Inverses
b) Inverses
Watch the Step by Step Video Solution
#2:
Solutions:
a) Not Inverses
b) Inverses
Watch the Step by Step Video Solution
#3:
Solutions:
a) Not Inverses
b) Inverses
Watch the Step by Step Video Solution
#4:
Solutions:
a) Inverses
b) Not Inverses
Watch the Step by Step Video Solution
#5:
Solutions:
a) Inverses
b) Not Inverses
