The one-to-one functions g and h are defined as follows. g =...

Transcript

00:01 Given the functions g is equal to the set of all negative 7 1 negative 2 2 7 negative 3 and 8 negative 2 and h of x to be the function 3x minus 13 the first question is to determine g inverse of negative 2 given that both these functions are 1 1 1 functions now the inverse function of a function exists if and only if the function is a bijection or the function is a bijective function that is it must be both one one and on two now it is given that the functions are one one and these two functions are on to as well because consider g it is having elements negative seven negative two seven and eight in the domain and its codomine is same as its range so since the codomine is same as its range its entire elements in the codomine will have a pre -image in the domain so that means the function is a bi -jection now the inverse function means it is the reverse mapping of g that means it will map the elements in the range set to the domain set so here see that since since 8 is mapped to negative 2 by g, the inverse function will map negative 2 back to 8.

01:40 So from here we can say the inverse of negative 2 is 8.

01:47 Therefore, this is a required first answer.

01:51 The next question is to find h inverse of x.

01:55 We have h of x is equal to 3x minus 13 is a 1 1 function.

02:01 Now this is a function from the set of all real numbers to the set of real numbers.

02:07 Now for any y element of the set of real numbers, if the function h is on to, we must have y is equal to h of x.

02:14 Now that means we have y must be equal to 3x minus 13.

02:18 From here we can solve for x as y plus 13 is equal to 3x...

Question

The one-to-one functions g and h are defined as follows. g = {(-7, 1), (-2, 2), (7, -3), (8, -2)} h(x) = 3x - 13 Find the following. g^-1(-2) = h^-1(x) = (h ? h^-1)(8) =

Question

The one-to-one functions g and h are defined as follows. g = {(-7, 1), (-2, 2), (7, -3), (8, -2)} h(x) = 3x - 13 Find the following. g^-1(-2) = h^-1(x) = (h ? h^-1)(8) =

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