let f : R --- R be defined by f(x)= x square + 1 , find 1) { x - Maths - Relations and Functions

Question

let f : R ---> R be defined by f(x)= x square + 1 , find
1) { x : f (x) = 26 }
2) the pre-image of 17

Harleen Birdi · Accepted Answer

$f (x) = x^{2} + 1 (1) f (x) = 26 \Rightarrow x^{2} + 1 = 26 \Rightarrow x^{2} = 25 \Rightarrow x = \pm 5 ∴ {x : f (x = 26} = {5, - 5}$

(2) Let x be preimage of 17.

$f (x) = 17 \Rightarrow x^{2} + 1 = 17 \Rightarrow x^{2} = 16 \Rightarrow x = \pm 4$

So, preimages of 17 are –4 and 4.

let f : R ---> R be defined by f(x)= x square + 1 , find 1) { x : f (x) = 26 } 2) the pre-image of 17