Composite functions Quiz 1

Question 1

Given $$f\left( x \right)={{x}^{2}}+3x,g\left( x \right)=\dfrac{2x+1}{x+2} $$,  Find  $$fg\left( x \right)$$.

Accepted Answer

$$\dfrac{2{{x}^{3}}+7{{x}^{2}}+3x}{x+2} $$

Answer

$$\dfrac{{{x}^{3}}+{{x}^{2}}+3x}{x+2} $$

Answer

$$\dfrac{4{{x}^{3}}+{{x}^{2}}+2x}{x+2} $$

Answer

$$\dfrac{4{{x}^{3}}+7{{x}^{2}}+3x}{x+2} $$

Question 2

If $$f\left( x \right)=\sqrt{{{x}^{3}}+x+8},g\left( x \right)=\sqrt[3]{5} $$,then  $$f\left( g\left( x \right) \right) $$

Accepted Answer

$$\sqrt{13+\sqrt[3]{5}} $$

Answer

$$\sqrt{10+\sqrt[3]{5}} $$

Answer

$$\sqrt{5+\sqrt[3]{5}} $$

Answer

$$\sqrt{8+\sqrt[3]{5}} $$

Question 3

What is the  $${{\dfrac{1}{3}}^{rd}} $$of  $$f\left( g\left( x \right) \right) $$, where  $$f\left( x \right)={{x}^{2}}+\dfrac{5}{9}\sqrt{x}-3,g\left( x \right)=9x $$.

Accepted Answer

$$27{{x}^{2}}+\dfrac{5\sqrt{x}}{9}-1 $$

Answer

$$9{{x}^{2}}+\dfrac{5\sqrt{x}}{3}-3 $$

Answer

$$9{{x}^{2}}+\dfrac{5\sqrt{x}}{9}-1 $$

Answer

$${{x}^{2}}+\dfrac{5\sqrt{x}}{9}-1 $$

Question 4

Given  $$f\left( x \right)=3x-\sqrt{x},g\left( x \right)={{x}^{2}}+7 $$, what is the value of  $$\left( f\circ g \right)\left( 5 \right) $$.

Accepted Answer

$$96-4\sqrt{2} $$

Answer

$$48-3\sqrt{2} $$

Answer

$$54-5\sqrt{2} $$

Answer

$$14-5\sqrt{2} $$

Question 5

If a function is given by  $$f\left( x \right)={{x}^{2}}+5x-6 $$ then find  $$f\left( g\left( x+3 \right) \right) $$ if  $$g\left( x \right) $$ here is the derivative of  $$f\left( x \right) $$.

Accepted Answer

$$4{{x}^{2}}+54x+170 $$

Answer

$${{x}^{2}}+45x+108 $$

Answer

$$2{{x}^{2}}+64x+120 $$

Answer

$$3{{x}^{2}}+45x+120 $$