SOLUTION: Which of the following functions have inverses: a) f(x)=absolute value of x-6 b) f(x)=ax + b, a not equal to 0 c) f(x)=x^3-19

Question 33774: Which of the following functions have inverses:
a) f(x)=absolute value of x-6
b) f(x)=ax + b, a not equal to 0
c) f(x)=x^3-19
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Which of the following functions have inverses:LET Y=F(X)
THIS MEANS FOR A GIVEN VALUE OF Y THERE SHOULD BE A UNIQUE X..OR.IF Y1=Y2 THEN X1=X2
a) f(x)=absolute value of x-6....IT HAS INVERSE IF WE DEFINE IT AS DUAL FUNCTION FOR DIFFERENT VALUES OF X.SINCE Y=|X-6|...OR..Y=X-6...IF X>6....THEN X=Y+6......BUT....Y=-(X-6)....IF X<6....THEN....X=-Y+6....IT SATISFIES THE ABOVE CONDITION..IF WE ADOPT THE FUNCTION DIFFERENTLY FOR DIFFERENT RANGES OF X..OTHERWISE,IT WILL NOT BE A FUNCTION OR WILL NOT HAVE AN INVERSE..SINCE FOR Y=3 X COULD BE -3...OR....3
b) f(x)=ax + b, a not equal to 0.....IT HAS INVERSE..SINCE X=(Y-B)/A..WITH A NOT EQUAL TO ZERO.
c) f(x)=x^3-19....IT HAS INVERSE IN REAL FIELD,BUT NOT IN COMPLEX FIELD..SINCE X=CUBE ROOT OF (Y+19) HAS UNIQUE ROOT IN REAL FIELD BUT 2 IMAGINARY AND 1 REAL ROOT IN COMPLEX FIELD.
RELATED QUESTIONS
Which of the following functions does not have a range of only the real numbers greater... (answered by MathLover1)

Find the equation of the inverse for each function. State which of the following inverses (answered by MathLover1)

Find the equation of the inverse for each function. State which of the following inverses (answered by Boreal)

Which of the following functions, if any, is an odd function? A) f(X)=3X^2+5 B) f(X)=... (answered by Shin123)

HELP: Given 2 functions f(x)-2x-5 and g(x)=x^2. Determine whether each of the following... (answered by CharlesG2,rapaljer)

consider the function f(x)=x^3-4 and g(x)=3 sqrt x+4 a. find f(g(x)) b. find g(f(x)) (answered by Theo)

Which of the following are functions? The last two problems, i.e., b & c, are multi part (answered by solver91311)

Which of the following are functions? The last two problems, i.e., b & c, are multi part (answered by Fombitz)

For each pair of functions f and g below, find f (g (x)) and g (f(x)) Then, determine... (answered by Theo)