Let f : R → R be defined by\(f(x)=\begin{cases}2x+3,&when& x<-2\\x^2

1.	Let f : R → R be defined by\(f(x)=\begin{cases}2x+3,&when& x<-2\\x^2-2,&when&-2\leq x\leq 3\\3x-1,&when&x>3\end{cases}\)Find (i) f(2) (ii) f(4) (iii) f( - 1) (iv) f( - 3).
Answer» i)f(2) Since f(x) = x² - 2 , when x = 2 ∴ f(2) = (2)² - 2 = 4 - 2 = 2 ∴f(2) = 2 ii)f(4) Since f(x) = 3x - 1 , when x = 4 ∴f(4) = (3×4) - 1 = 12 - 1 = 11 ∴f(4) = 11 iii)f( - 1) Since f(x) = x²- 2 , when x = - 1 ∴ f( - 1) = ( - 1)² - 2 = 1 - 2 = - 1 ∴f( - 1) = - 1 iv)f( - 3) Since f(x) = 2x + 3 , when x = - 3 ∴f( - 3) = 2×( - 3) + 3 = - 6 + 3 = - 3 ∴f( - 3) = - 3

Let f : R → R be defined by\(f(x)=\begin{cases}2x+3,&when& x<-2\\x^2-2,&when&-2\leq x\leq 3\\3x-1,&when&x>3\end{cases}\)Find (i) f(2) (ii) f(4) (iii) f( - 1) (iv) f( - 3).

Answer»

i)f(2)

Since f(x) = x² - 2 , when x = 2

∴ f(2) = (2)² - 2 = 4 - 2 = 2

∴f(2) = 2

ii)f(4)

Since f(x) = 3x - 1 , when x = 4

∴f(4) = (3×4) - 1 = 12 - 1 = 11

∴f(4) = 11

iii)f( - 1)

Since f(x) = x²- 2 , when x = - 1

∴ f( - 1) = ( - 1)² - 2 = 1 - 2 = - 1

∴f( - 1) = - 1

iv)f( - 3)

Since f(x) = 2x + 3 , when x = - 3

∴f( - 3) = 2×( - 3) + 3 = - 6 + 3 = - 3

∴f( - 3) = - 3