Math AA SL: Basic Functions

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[Maximum Marks: 6]

f(x)=12-4x and g(x)=x-5

a) Find f\circ{g}

b) Find g^{-1}

c) Find g^{-1}\circ{f}
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 4] 

Let f(x)= 12x and let g(x)=2x^{2}+3, x \in \mathbb{R}

a) What is f^{-1}(x)?

b) What is (f \circ g)(2)?
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 5]

f(x)= 16x+6 and g(x)= 8x, where x \in \mathbb{R}

a) Find g(2)

b) Find (f \circ g)(x)

c) Find f^{-1}(x)
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 6]

f(x)= \sqrt{x+6} and h(x)= 10x+3

a) Find f(10)

b) Find (h \circ f)(10)

c) Find h^{-1}(x)
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 8]

Let f(x)=6x+1 and g(x)=2x, \forallx\in \mathbb{R}

a) What is g(5) 

b) Find (f \circ g)(x) 

c) Find f^{-1}(x)
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 6] 

Let f(x)=3x-2 and g(x)=2x^2+5

a) Find f^{-1}(x).

b) Find (f\circ{g})(1).
Detailed Answer/Video Explanations Answer
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[Maximum Marks: 5]

Let f(x)=5x, g(x)=x+8 and h(x)=(f \circ\ g)(x).

a. Find h(x).

b. Find h^{-1}(x).
Detailed Answer/Video Explanations Answer
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[Maximum Marks: 7]

Consider the function f(x)=\log_{2}\sqrt{x}, for x>0.

a) Show that f^{-1}(x)=2^{2x}.

b) What is the range of f^{-1}?

c) Let g(x)=\log_{4}(x), for x>0.

Find the value of (f^{-1}\circ{g})(3), and provide your answer as an integer.
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 7]

Let f(x)=klog_2x
 
a) Given f^{-1}(2)=16, Solve for k
 
b) Find f^{-1}(1)
Detailed Answer/Video Explanations Answer
#MAASL00189

[Maximum Mark: 5]

Let f(x)=5x , g(x)=3x-2 and h(x)=(f \circ g)(x)

a) Find h(x)

b) Find h^{-1}(x)
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 5]

Let f(x)=4x , g(x)=6x-3 and h(x)=(f \circ g)(x)

a) Find h(x)

b) Find h^{-1}(x)
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 5]

Let f(x)=10-2x and g(x)=x+2

a) Find (g \circ f)(x)

b) Write down g^{-1}(x)

c) Find (f \circ g^{-1})(2)
Detailed Answer/Video Explanations Answer
#MAASL00192

[Maximum Mark: 5]

Let f(x)=8-4x and g(x)=x+6

a) Find (g \circ f)(x)

b) Write down g^{-1}(x)

c) Find (f \circ g^{-1})(3)
Detailed Answer/Video Explanations Answer

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