Question

7 (b) 16 7 22 7 6 7 (d) If (ax + 1) (bx-3)=6x² + cx-3 for all values of x and a+b=5, what are the two possible values for c?​

Answer 1

Answer:

The value is f(7)=-17.

Step-by-step explanation:

Given : Function f(x)=ax^7+bx^3+cx-5f(x)=ax

7

+bx

3

+cx−5 where a,b and c are constants. If f(-7)=7.

To find : The value of f(7) ?

Solution :

f(x)=ax^7+bx^3+cx-5f(x)=ax

7

+bx

3

+cx−5

Substitute x=-7,

f(-7)=a(-7)^7+b(-7)^3+c(-7)-5f(−7)=a(−7)

7

+b(−7)

3

+c(−7)−5

-a(7)^7-b(7)^3-c(7)-5=7−a(7)

7

−b(7)

3

−c(7)−5=7 ....(1)

Substitute x=7,

f(7)=a(7)^7+b(7)^3+c(7)-5f(7)=a(7)

7

+b(7)

3

+c(7)−5

a(7)^7+b(7)^3+c(7)-5=xa(7)

7

+b(7)

3

+c(7)−5=x ....(2)

Add equation (1) and (2),

-a(7)^7-b(7)^3-c(7)-5+a(7)^7+b(7)^3+c(7)-5=7+x−a(7)

7

−b(7)

3

−c(7)−5+a(7)

7

+b(7)

3

+c(7)−5=7+x

-10=7+x−10=7+x

x=-17x=−17