show that the given function is onetoone and find its invers

show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the domain of f 1 and vice-versa.

2. f(x)=42x

Solution

f(x) = 42 -x

A function for which every element of the range of the function corresponds to exactly one element of the domain.

if f(a) = f(b)

42 -a = 42 -b

a = b. Thus f(x) is 1-1

Inverse: y = 42 -x

Replace x with y and y with x and solve

y = 42 -x

x = 42 -y

y = 42 -x

So, f(x) = f^-1(x)

Domain :All real ( - inf , inf)

Range :All real ( - inf , inf)