Let f : R → R defined by $f(x)=2 x^3-7$ for $x \in R$. Then :
(A) f is one-one function
(B) f is many to one function
(C) f is bijective function
(D) f is into function
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) - (A) and (C) only
for $y=2x^3-7⇒\frac{(y+7)^{\frac{1}{3}}}{2}=x$
for every y atleast some x exists (ONTO function)
for $y_1=y_2$
$2x_1^3-7=2x_2^3-7$
so $x_1^3=x_2^3⇒x_1=x_2$ always (ONE ONE)
⇒ it is bijective