Q 25. - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of the composite function  $f\circ g$.

$f\left(x\right)=\sqrt{x} and g\left(x\right)=2x+3$

Step-by-Step Solution

Answer

Domain of the composite function of $f\left(x\right)=\sqrt{x} and g\left(x\right)=2x+3$ is $[0, \infty )$.

Step 1. Given information.

We have given,

$f\left(x\right)=\sqrt{x} and g\left(x\right)=2x+3$

Step 2. Concept used.

Domain is the set of all input values where the function is well defined and real.

Step 3. Explanation.

We have given,

$f\left(x\right)=\sqrt{x} and g\left(x\right)=2x+3$

g(x) is the polynomial function and domain of polynomial function is the set of all real numbers.

So domain of the g(x) is the set of all real numbers.

Similarly domain of the f(x) is $[0, \infty )$.

So we need to exclude from the domain of g(x).

So domain of composite function of $f\left(x\right)=\sqrt{x} and g\left(x\right)=2x+3$ is $[0, \infty )$

Step 4. Conclusion.

Hence, domain of the composite function of $f\left(x\right)=\sqrt{x} and g\left(x\right)=2x+3$ is $[0, \infty )$.