<span><span><span>Given <span>f(x) = 2x + 3</span><span> and </span><span>g(x) = –x2 + 5</span><span>, find </span></span><span>(<span> f</span> </span>o<span> f )(x</span><span>).</span></span><span>(<span> f</span> </span>o<span> <span>f </span>)(x) = f (<span> f</span> (x))</span><span>
</span><span> = f (2x + 3)</span><span>
</span><span> = 2( ) + 3 </span>... setting up to insert the input<span>
</span><span> = 2(2x + 3) + 3</span><span>
</span><span> = 4x + 6 + 3</span><span>
</span> <span>= 4x + 9</span></span><span><span><span><span>Given </span><span>f(x) = 2x + 3</span><span> and </span><span>g(x) = –x2 + 5</span><span>, find </span></span><span>(g</span><span> o</span><span> g)(x</span><span>).</span></span><span>(g </span>o<span> g)(x) = g(g(x))</span><span>
</span><span> = –( )2 + 5 </span>... setting up to insert the input<span>
</span><span> = –(–x2 + 5)2 + 5</span><span>
</span><span> = –(x4 – 10x2 + 25) + 5</span><span>
</span><span> = –x4 + 10x2 – 25 + 5</span><span>
</span><span> = </span><span>–x4 + 10x2 – 20</span></span>
Sometimes you have to be careful with the domain and range of the composite function.
<span><span><span>Given </span><span>f (x) = sqrt(x)</span><span> and </span><span>g(x) = x – 2</span><span>, find the domains of </span><span>(<span> f</span> </span>o<span> g)(x)</span><span> and </span><span>(g </span>o<span> f )(x)</span>.</span></span>
Answer:
8000
Step-by-step explanation:
I did a simple way, I divided 4800 by 3 and got 1600, then multiplied 1600 by 5. Because 2x5 =10 (or 100%)
Answer:
Step-by-step explanation:
Upon factoring all terms we are left with the product of
[(x-4)(x+6)(x-6)]/[5(x-6)(3x+5)(x-4)]
The (x-4)s and (x-6)s cancel out and we are left with
(x+6)/(5(3x+5)) which is also equal to
(x+6)/(15x+25)
Answer:
Step-by-step explanation:
we will use first the distributive property and multiply
45+ 5a<110
subtract 45 from both sides
5a<110-45
5a<65 we divide by 5
a<13
