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mihalych1998 [28]
3 years ago
7

Prove that f(x)=x+3/2 and g(x)=2x-3are inverse

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
5 0

Answer:

Proofs

Step-by-step explanation:

f(x) = x +  \frac{3}{2}

y = x +  \frac{3}{2}

x = y +  \frac{3}{2}

x -  \frac{3}{2}  = y

{f}^{ - 1} (x) = x -  \frac{3}{2}

They are not inverse because f^-1(x) = x - 3/2 is not the inverse to g(x) = 2x - 3.

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Let x be the number of pounds of the $1.35 beans. The cost of those beans is $1.35 * x, or 1.35x. 
<span>Let y be the number of pounds of the $1.05 beans. The cost of those beans is $1.05 * y, or 1.05y. </span>
<span>We know that 120 pounds of the mix sells for $1.15/pound, for a total of 120 * 1.15 = $138. </span>

<span>x + y = 120 </span>
<span>1.35(x) + (1.05)y = 138 </span>

<span>We can rewrite the first as </span>
<span>x = -y + 120 </span>

<span>Now we can substitute (-y + 120) in for (x) in the second equation, because we just proved they're equal. </span>

<span>1.35(x) + 1.05(y) = 138 </span>
<span>1.35(-y + 120) + 1.05y = 138 </span>
<span>-1.35y + 162 + 1.05y = 138 </span>
<span>-0.3y + 162 = 138 </span>
<span>-0.3y = -24 </span>
<span>y = 80 </span>

<span>And since x + y = 120, that means x = 40. </span>

<span>Check: </span>
<span>40 pounds of x at $1.35 costs 40 * 1.35, or $54. </span>
<span>80 pounds of y at $1.05 costs 80 * 1.05, or $84. </span>
<span>Do those add up to our target total, according to the question, of 120 * 1.15 = $138? </span>
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