Question

3) Which one of the following functions is a 1-1 function? A) 5(x)=(x+3| B) f(x)=x²-4 C) f(x) = 3x +5 D) S(x)=5–x?

Answer 1

Answer : C

Solution : A function is said to be 1 -1 function , if distinct elements of first set have distinct images in other set.

Keeping this is in mind let us consider every options.

(Further solution is attached as image as it is difficult to solve mathematics via keyboard.)
3) which one of the following functions is a 1-1 Function a) f(a) – 12+31 Let us consider the value for f(-2) and f(-4) in the above function. f(-2) – 1-2+31 = 111 - 1 f(-4) = 1-4+31 - 1-1 =1 that means the two elements (-2),(-4). have same timage je 24-4 but f(2)=f(4) ce f(x) = 12+31 is not 1-1 function b) f(x) = 2-4 Let f(x) = f(x) Now f(y): 2-4 E d?-4 = 42-4 012-Y2 x=IY Hence

a since à has two images je ty and -1 Thus the function f(x) = R-4 is not a one-one function. flu) - 34+5 Let us assume f(3) = f(0) fly) - 34+5 According to our assumptious 32+5=37+5 - 3x = 341 > a = Y Since & had a unique image 1 the function f(x) = 32+5 is a. 1-1 (one-one) function. Fla) - 5-x? Let f(x) = f (y) fly) - 5-12 5-2? = 5-12 W?=y? n=IY a) 9 11 its or 11

- Since à has two images sety and - Thus the function f(x) = 5-2? is not a 1-1 function.