1
KCET 2024
MCQ (Single Correct Answer)
+1
-0

Let the function satisfy the equation $f(x+y)=f(x) f(y)$ for all $x, y \in R$, where $f(0) \neq 0$. If $f(5)=3$ and $f^{\prime}(0)=2$, then $f^{\prime}(5)$ is

A
6
B
0
C
3
D
$-$6
2
KCET 2023
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=a x+b$$, where $$a$$ and $$b$$ are integers, $$f(-1)=-5$$ and $$f(3)=3$$, then $$a$$ and $$b$$ are respectively

A
$$2,-3$$
B
$$0,2$$
C
$$2,3$$
D
$$-3,-1$$
3
KCET 2023
MCQ (Single Correct Answer)
+1
-0

$$f: R \rightarrow R$$ and $$g:[0, \infty) \rightarrow R$$ defined by $$f(x)=x^2$$ and $$g(x)=\sqrt{x}$$. Which one of the following is not true?

A
$$(f \circ g)(-4)=4$$
B
$$(f \circ g)(2)=2$$
C
$$(g \circ f)(-2)=2$$
D
$$(g \circ f)(4)=4$$
4
KCET 2023
MCQ (Single Correct Answer)
+1
-0

Let $$f: R \rightarrow R$$ be defined by $$f(x)=3 x^2-5$$ and $$g: R \rightarrow R$$ by $$g(x)=\frac{x}{x^2+1}$$, then $$g \circ f$$ is

A
$$\frac{3 x^2-5}{9 x^4-6 x^2+26}$$
B
$$\frac{3 x^2}{x^4+2 x^2-4}$$
C
$$\frac{3 x^2}{9 x^4+30 x^2-2}$$
D
$$\frac{3 x^2-5}{9 x^4-30 x^2+26}$$
KCET Subjects
EXAM MAP