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3 years ago

Find the values of the unknown constants for the identities

Mathematics

1 answer:

ankoles [38]3 years ago

5 0

Answer:

a = 1 and b = - 10

Step-by-step explanation:

Expand the right side of the identity

x(ax² - 3x + b) - 3(ax² - 3x + b)

= ax³ - 3x² + bx - 3ax² + 9x - 3b

= ax³ - x²(3 + 3a) + x(b + 9) - 3b

Equate the coefficients of like terms on both sides of the identity

x³ terms → ax³ with x³ ⇒ a = 1

x terms → - x with (b + 9)x ⇒ b + 9 = - 1 ⇒ b = - 10

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Step-by-step explanation:

Since we have given that

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b) . Use composition to show that f(x) and g(x) are inverses of each other.

$\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x$

Similarly,

$\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x$

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c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

And both f(x) and g(x) are symmetry to y=x.

∴ f(x) and g(x) are inverses of each other.

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denis23 [38]

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2 years ago