# 4. Given the following function find its inverse. Specify the domai...

## Question

4. Given the following function find its inverse. Specify the domain and range of the inverse.
f: R → R given by f(x) = x³

5. Show that the function f : A → R is one-to-one. Find the range.
A = { x ∈ R | x ≠ -1}, f(x) = 5 – 1 / ( 1 + x)

6. Find a one-to-one correspondence between each of the following pairs of sets:
a) {x, y, {a, b, c}} and {14, -3, t}
b) 2Z and 17Z

7. Let f = {(1, 2), (2, 3), (3, 4) , (4, 1) and g = {(1, 3), (2, 1), (3, 4), (4, 2), (5, 1)}.
Find f-1 and g ° f. Is g one-to-one? Explain.

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