Question

Let f : R → R and g : R → R be functions defined by f(x) = 5 – x² and g(x) = 3x – 4. Then the value of fog (–1) is ___________.

Answer 1

Given: f(x) = 5 – x² and g(x) = 3x – 4


$$\begin{gathered} fog\left(-1\right)=f\left(g\left(-1\right)\right) \\ =f\left(3\left(-1\right)-4\right) \\ =f\left(-3-4\right) \\ =f\left(-7\right) \\ =5-{\left(-7\right)}^2 \\ =5-49 \\ =-44 \end{gathered}$$


Hence, the value of fog (–1) is ​–44.