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svp [43]
2 years ago
8

Given: f(x)=x^2 g(x)=x-1 Find f(g(2))+g(f(-1))

Mathematics
1 answer:
Marina CMI [18]2 years ago
8 0

Answer:

-1

Step-by-step explanation:

First, we need to work out the left-hand side.

  • find g(2) → g(2) = 2 - 1 which is 1
  • next, find f(1) → f(1) = 1³ which is 1

Now, we can work out the right hand side.

  • find f(-1) → f(-1) = -1³ which is -1
  • then, find g(-1) → g(-1) = -1 - 1 = -2

Finally we can work out the full sum: 1 + -2 = -1.

Hope this helps!

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12345 [234]

Answer:

<em>19</em>

Step-by-step explanation:

f(x) =4x^3-8x^2+ax+b has a factor 2x-1 and

when divided by x+2, remainder is 20.

To find:Remainder when divided by (x-1)  ?

Solution:

2x-1 is a factor

2x - 1 = 0 \Rightarrow x = \frac{1}{2} when we put this value of x to the function, it will become 0.

i.e.

\Rightarrow f(\dfrac{1}{2}) =0 =4\times (\dfrac{1}2)^3-8(\dfrac{1}2)^2+\dfrac{a}{2}+b=0\\\Rightarrow \dfrac{1}{2}-2+\dfrac{a}{2}+b=0\\\Rightarrow 1-4+a+2b=0\\\Rightarrow a +2b=3 ......(1)

Remainder is 20 when f(x) is divided by x+2

i.e.

f(-2) =20

\Rightarrow f(-2) =20 =4\times (-2)^3-8(-2)^2-2a+b=20\\\Rightarrow -32-32-2a+b=20\\\Rightarrow -2a+b=84 ...... (2)

Solving (1) and (2), Multiply equation (1) by 2 and adding to (2):

5b=6+84\\\Rightarrow b = \dfrac{90}{5} = \bold{18}

By equation (1):

a+2(18) = 3\\\Rightarrow a = -33

So, the equation becomes:

f(x) =4x^3-8x^2-33x+18

\Rightarrow f(1) = 4(1) -8 (1) -33(1) +18 = \bold{19}

So, when divided by (x-1), remainder will be <em>19</em>.

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