Solve this: Q 8 Let X = Y = [- 1, 1] For each of the following functions - Maths - Relations and Functions

Question

Solve this:
Q 8 Let X = Y = [- 1, 1] For each of the following functions from X
to Y, state whether it is onto or into
(a) f(x) = x 2
(b) g (x) = | x |
(c) h (x) = x | x |
(d) f (x) = sin π x

Aarushi Mishra · Accepted Answer

X=Y=-1,1f:X→Yafx=x2f'x=12fx is increasing-1≤x≤1f-1≤fx≤f1-12≤fx≤12Range≠ co-domainIt is into functionbgx=xx≥0gx≥0Range≠ co domaininto fuinctionc hx=xxhx=x2,   x≥0-x2,   x<0Observe hx is continuous h1=12=1h-1=-12=-1Since hx is continuous, so it will take all values between -1 and 1
onto functiondfx= sin πxAt x=12fx=sin π2=1At x=-12fx=sin -π2=-1Since fx is continuous, so it will take all values between -1 and 1
onto function

Solve this: Q.8. Let X = Y = [- 1, 1]. For each of the following functions from X to Y, state whether it is onto or into. (a) f(x) = x 2 (b) g (x) = | x | (c) h (x) = x | x | (d) f (x) = sin π x

Solve this:
Q.8. Let X = Y = [- 1, 1]. For each of the following functions from X to Y, state whether it is onto or into.
(a) f(x) = $\frac{x}{2}$
(b) g (x) = | x |
(c) h (x) = x | x |
(d) f (x) = sin $π$ x