Functions and Relations MCQs with Answers

Find $g \circ f$, if $f(t) = \frac{1}{t}$ and $g(t) = t^3$.

• A.$g \circ f(t) = \frac{1}{t^3}$
• B.$g \circ f(t) = t^3$
• C.$g \circ f(t) = \frac{3}{t}$
• D.$g \circ f(t) = \frac{t^3}{3}$

If $x = -1$, then what is the value of the function $f(x) = x^3 + 3x + 9$?

• A.$11$
• B.$7$
• C.$5$
• D.$13$

If set $A$ contains 2 elements and set $B$ contains 3 elements, how many relations can be formed from $A \times B$?

• A.$2^5 = 32$
• B.$2^6 = 64$
• C.$2^3 = 8$
• D.$6^2 = 36$

The converse of the contrapositive of $p \to q$ is?

• A.$\neg q \to \neg p$
• B.$q \to p$
• C.$p \to q$
• D.$\neg p \to \neg q$

If $g(t) = t^3 + t^2 - 9t - 9$, then $g(3) =$ ?

• A.$0$
• B.$3$
• C.$9$
• D.$18$

If $f(x) = x^2$ and $g(x) = 2x$, then $f(g(x)) = \text{_}$?

• A.$4x^2$
• B.$2x^2$
• C.$2x^3$
• D.$x^2 + 2x$

Which of the following statements best represents the relationship between a function and an equation?

• A.Every equation is a function and every function is an equation
• B.All equations are functions, but not all functions are equations
• C.Functions and equations are completely unrelated concepts
• D.All functions are equations, but not all equations are functions

If $x = -1$, then what is the value of the function $f(x) = x^3 + 4x + 12$?

• A.$7$
• B.$15$
• C.$9$
• D.$17$

If $f: A \to B$ is a one-one function, it is called a:

• A.Bijective function
• B.Surjective function
• C.Injective function
• D.Constant function

If $f(x) = x^2 - 2x^3$, what is the value of $f(3)$?

• A.$-45$
• B.$-9$
• C.$45$
• D.$9$