Chapter 5: Q. 61 (page 257)

If $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 23.

Short Answer

Expert verified

The value of $a$ is $\pm 3 .$

Step by step solution

Step 1. Given Information

Given that $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a,$ value of $f \circ g (x) = 23$ at $x = 0 .$

Step 2. Solution

We know that $f \circ g (x) = f (g (x)) .$

Here, $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a .$

So, $f \circ g (x) = f (g (x)) f \circ g (x) = 2 (g {(x))}^{2} + 5 f \circ g (x) = 2 {(3 x + a)}^{2} + 5 f \circ g (x) = 2 {9 x^{2} + 6 x a + a^{2}} + 5 f \circ g (x) = 18 x^{2} + 12 x a + 2 a^{2} + 5$

So, at $x = 0$ , $f \circ g (x) = 23 .$

Now,

$a t x = 0, f \circ g (0) = 18 {(0)}^{2} + 12 (0) (a) + 2 a^{2} + 5 23 = 0 + 0 + 2 a^{2} + 5 2 a^{2} = 18 a^{2} = 9 a = \pm 3 .$

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If $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 23.

Short Answer

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Step 1. Given Information

Step 2. Solution

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If f(x)=2x2+5and g(x)=3x+a, find a so that the graph of f∘g crosses the y-axis at 23.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

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If $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 23.