Question

Let $f\left(x\right)$ and $g\left(x\right)$ be bijective functions where $f:\{a,b,c,d\}\to \{1,2,3,4\}$ and $g:\{3,4,5,6\}\to$ $\{w,x,y,z\},$ respectively. Then, the number of elements in the range set of $g\left(f\right(x\left)\right)$ is

• A. 2.0
• B. 2
• C. 2.00

Answer 1

Answer: (A), (B), (C)

The range of $f\left(x\right)$ for which $g\left(f\right(x\left)\right)$ is defined is $\{3,4\}$
Hence, the domain of $g\left\{f\right(x\left)\right\}$ has two elements.

$\therefore$ The number of elements in the range of $g\left(f\right(x\left)\right)$ also has two elements.