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Scalar Matrix

If fx=a x+b a...

Question

If f(x) = ax + b and g(x) = cx + d, then f[g(x)] – g[f(x)] is equivalent to

A

f(b) – g(b)

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B

f(c) + g(a)

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C

f(a) – g(c)

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D

f(d) – g(b)

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Solution

The correct option is D
f(d) – g(b)

f(g(x)–g(f(x)) = a(cx + d) + b – {c(ax + b) + d}

= ad + b – bc – d = (ad + b) – (bc + d) = f(d) – g(b)

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Similar questions

f (x) = a x + b

g (x) = c x + d

f (g (x)) = g (f (x)) \Leftrightarrow

f (x) = a x + b

g (x) = c x + d

f (g (x)) = g (f (x))

f (x) = a x + b

g (x) = c x + d

f (g (x)) = g (f (x)),

then which one of the following is correct?

f (x) = x^{2}

g (x) = 2 x - 6

, find the following functions:

(f + g) (x), (f \times g) (x), (f \circ g) (x), (f \circ f) (x), g^{- 1} (x)

f (x) = - 9 x^{3}

g (x) = - 3 x

then choose the correct options
[Given :

(f . g) (x) = f (x) . g (x), (f / g) (x) = f (x) / g (x)

]

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