If h(x) = 5 + x and k(x) = 1/x, what expression is equivalent to (k × h)(x)?

Solution:

Given, h(x) = 5 + x

k(x) = 1/x

We have to find the expression equivalent to (k×h)(x).

(k × h)(x) = k(x) × h(x)

= 1/x × (5 + x)

Using the distributive property

= 5/x + 1

Therefore, the expression equivalent to (k × h)(x) is 5/x + 1.

Example:

If h(x) = x - 7 and g(x) = x² which expression is equivalent to (g × h)(5)

Solution:

Given, h(x) = x - 7

g(x) = x²

We have to find (g × h)(5).

(g × h)(x) = g(x) × h(x)

= x² × (x - 7)

= x³ - 7x²

Now, put x = 5 in the above expression,

(g × h)(5) = 53 - 7(5)² = 125 - 175 = -50

Therefore, the expression equivalent to (g × h)(5) is -50.

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If h(x) = 5 + x and k(x) = 1/x, what expression is equivalent to (k × h)(x)?

Summary:

If h(x) = 5 + x and k(x) = 1/x, the expression equivalent to (k × h)(x) is 5/x + 1.