Find the inverse of f. Determine the domain and range of each resulting inverse functions.
3. f(x) = x+2
Solution:
y = x+2
interchange x and y;
x = y+2
subtract 2 to both sides of the equation;
x-2 = y
rewrite y as f^-1(x);
[tex]Answer = f^-1(x) = x-2[/tex]
[tex]Domain = {X|x∈ℝ}[/tex]
[tex]Range = {X|x∈ℝ}[/tex]
4. f(x) = x² + 2
Solution:
y = x² + 2
interchange x and y;
x = y² + 2
subtract 2 to both sides of the equation;
x-2 = y²
take the square root of both sides of the equation;
√(x-2) = √(y)²
the square root and the 2 power degree of y will negate;
y = √(x-2)
rewrite y as f^-1(x);
[tex]Answer = f^-1(x) = \sqrt{(x-2)}[/tex]
[tex]Domain = {X| x \geqslant 2}[/tex]
[tex]Range \: = Y|y \geqslant 0[/tex]
5. f(x) = √1+x
Solution:
y = √1+x
interchange x and y;
x = √1+y
square both sides of the equation;
x² = 1+y
subtract 1 to both sides of the equation;
x²-1 = y
rewrite y as f^-1(x);
[tex]Answer = f^-1(x) = x²-1[/tex]
[tex]Domain=X∣x∈R[/tex]
[tex]Range = Y|y≥-1[/tex]
