Two functions represent the composite function h(x) = (x – 1)³ + 10 so that h(x) = (g compose f)(x). Given f(x) = x + a and g(x) = x³ + b, what values of a and b would make the composition true?

Step-by-step explanation:

Given the function  h(x) = (x – 1)³ + 10 so that h(x) = (g°f)(x). If f(x) = x + a and g(x) = x³ + b, then;

g(f(X)) = g(x+a).

To get g(x+a), we will have to replace the variable x with x+a in g(x) as shown;

g(x+a) =  (x+a)³ + b

g(f(x)) =  (x+a)³ + b

Since h(x)= g(f(x)) = (x – 1)³ + 10

g(f(x)) = (x+a)³ + b = (x – 1)³ + 10

Hence  (x+a)³ + b = (x – 1)³ + 10

On comparing the coefficients to get the value of a and b;

(x+a)³  = (x-1)³

Take the cube root of both sides

∛(x+a)³  = ∛(x-1)³

x+a = x-1

x+a-x = -1

a = -1

Also on comparing, b = 10

Hence the values of a and b would make the composition true are -1 and 10 respectively.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

2 apples

step-by-step explanation:

taking away equals subtraction. 6-4=2