A function f:R→R defined by f(x)=5x^4+2 is one – one but not

a-function-f-r-r-defined-by-f-x-5x-4-2-is-one-one-but-not

A function f:R→R defined by f(x)=5x^4+2 is one – one but not onto.
A. True
B. False

Correct choice is B. False

The above statement is false. f is neither one-one nor onto.
For one-one: Consider f(x1)=f(x2)

∴ 5×1^4+2=5×2^4+2

⇒x1=± x2.

Hence, the function is not one – one.
For onto: Consider the real number 1 which lies in co- domain R, and let $$x=(\frac{y-2}{5})^{\frac{1}{4}}$$

Clearly, there is no real value of x which lies in the domain R such that f(x)=y.

Therefore, f is not onto as every element lying in the codomain must have a pre- image in the domain.